Simplify: $\frac{2^{n+4} - 2(2^n)}{2(2^{n+3})}$. Express your answer as a common fraction.
Answer: Note that $\frac{2^{n+4} - 2(2^n)}{2(2^{n+3})} = \frac{2^n}{2^n}\cdot\frac{2^4 - 2}{2(2^3)} = \boxed{\frac{7}{8}}$.